Combined Public Key Algorithm

  • The combined public key algorithm (CPK) is an identity-based large-scale key management algorithm.
  • It can be used on any system that uses public key cryptography that has a special composite property.
  • Because typical blockchain systems use elliptic curve cryptography, which has this special composite property, the combined public-key algorithm can be applied to blockchain wallets to solve large-scale key management problems.

Algorithm

Let

PrivateSequence=(d1,d2,…,d𝑘)PublicSequence=(P1,P2,..,P𝑘)=(d1𝐺,d2𝐺,…,d𝑘𝐺)T=IdentifierSelectorSequence=(a1,a2,…,ak)=Mapping(T)\begin{align} PrivateSequence &= (d_1,d_2,\dots,d_𝑘) \\ PublicSequence &= (P_1,P_2,..,P_𝑘)=(d_1𝐺,d_2𝐺,\dots,d_𝑘𝐺) \\ T &= Identifier \\ SelectorSequence &= (a_1,a_2,\dots,a_k) = Mapping(T)\\ \end{align}

Then

ComposedPrivKeyi=∑j=1kaidi(modn)ComposedPubKeyi=∑j=1kaiPi\begin{align} ComposedPrivKey_i &= \sum_{j=1}^{k}a_id_i \pmod{n} \\ ComposedPubKey_i &= \sum_{j=1}^{k}a_iP_i \end{align}

Flowchart

Composed Private Key Generation

Private Sequence
(d1,d2,...,dk)
Identifier
Mapping Function
Selector Sequence
(a1,a2,...,ak)
Modular Multiplication
(a1d1, a2d2,...,akdk)
Modular Sum
a1d1 + a2d2 + ...+ akdk (mod n)
Composed Private Key

Composed Public Key Generation

PubSeq
(P1,P2,...,Pk)
Identifier
Mapping Function
Selector Sequence
(a1,a2,...,ak)
Point Scalar Multiplication
(a1P1, a2P2,...,akPk)
Point Sum
a1P1 + a2P2 + ...+ akPk
Composed Public Key

See Also

  1. CPK Blockchain Wallets